A physical gel is a three-dimensional network of polymer chains cross-linked by physical junctions

and it can arise either as the result of a phase transition or through some specific molecular association or as a result of entanglements. Due to the complexity of the inner structure and gelation mechanism

it is difficult to obtain purposefully polymer physical gel materials with specific constitution and properties. Thus

the controllable preparation and application of polymer physical gels are a long-term work.As a numerical simulation method in macro-scale the finite element method has been used to the study of chemical gelation

but rarely to physical gelation presently. The reasons may be: compared with chemical gels the gelation process of physical gels is more complex resulting from the bigger complexity of the system composition and physical interactions. Several kinds of interactions and steps may be involved in one physical gelation process. And under different conditions the gelation mechanisms are frequently different. By now the understanding of the gelation mechanisms of many kinds of physical gels is far from being intensive; the phenomenological gelation kinetics models are usually nonlinear; the theory describing the relation between the microscopic and mesoscopic structure and the macroscopic properties is still immature. For all the factors mentioned above the numerical simulation of physical gelation process in macro-scale comes to be a difficult work. In order to optimize raw material formulation and physical gelation conditions

and then obtain polymer physical gels according to requirements

the spatial distribution and time evolution characteristics of the temperature field during the gelation process were studied via the finite element method. On the basis of the temperature field calculated

the complex shear modulus field of gel system was numerically simulated according to a first-order gelation kinetic equation

and the effects of raw material concentration

sample size and cooling modes on the physical gelation were discussed.Rennet casein gel is a kind of particle gel

whose formation is controlled by physical forces including steric-hydration force and van der Waals force

and whose structure and properties are influenced by many parameters including emulsifying salts

pH

thermal and shear history.The formation process of the gel network can be divided into three steps

molecules-particles-flocs-network. Casein flocs are fractal objects that can be partially filled by the constructing units (particles).The fractal dimension of the flocs and the size of the particles are two important parameters determining the gel microscopic structure and rheological properties. Experimental results show that cooling modes will influence the rheological properties of the gel through influencing the size of the particles. The formation of rennet casein gels is a first-order kinetics process.Three examples were studied. The raw material concentrations of example 1 and example 2 are both 18%

but the sample size of the former is five times as that of the latter; the raw material concentration of example 3 is 25%

and the sample size is same with example 1. The gel zone is divided into 136 unites and 163 nodes; the prototype zone is divided into 28 unites and 40 nodes; four representative nodes were selected in the gel zone

and were emphatically studied. The initial system temperature is set at 80℃

and cooling modes include (1) environmental temperature declines from 80℃ to 5℃

and cooling rates are respectively 0.5 K/min

0.25 K/min

0.1 K/min

0.05 K/min

0.025 K/min; (2) environmental temperature maintains 5℃.The simulated results show that (1) the rate of temperature decrease near the surface is larger than that near the center

the gelation occurs on the surface first; as the infinite complex shear modulus is determined by the cooling rate of the pre-gelation phase

the value of the complex shear modulus of the interior exceeds that of the exterior finally. The asymmetric distribution of temperature field results in the asymmetric distribution of mechanical property field of the gel. And with the increase of environmental cooling rate and sample size the asymmetry becomes more obvious.